This invention relates to a linear time counter indicating a tape running amount.
Mathematical means for calculating a reel rotational angle to precisely determine a tape running amount on the basis of the calculated value, and approximation means for approximating a tape running time from the reel rotation number are known.
The mathematical means will be first described.
In the schematic diagram showing the tape winding relationship of FIG. 1, when it is assumed that a tape T moves by the length L from a supply reel 11 having a radius r.sub.L of the tape roll W.sub.L to a take-up reel 12 having a radius r.sub.R of the tape roll W.sub.R, and at that time the supply side reel 11 rotates by an angle .theta..sub.L and the takeup reel 12 rotates by an angle .theta..sub.R, the length L is expressed by the following relationships. EQU L=r.sub.L .theta..sub.L ( 1) EQU L=r.sub.R .theta..sub.R ( 2)
where the units of .theta..sub.L and .theta..sub.R are radian. Since the sum of the areas of the wound tape and the areas of the hubs of the supply reel 11 and the take-up reel 12 is always constant, the following relationship holds: EQU r.sub.L.sup.2 +r.sub.R.sup.2 =k (k is constant) (3)
In this case, k is given by the following equation: EQU k=(tape thickness.times.tape length+areas of the both hubs)/.pi.
In the case of C-60 of a normal or chrome tape, since the tape width is 18 .mu.m, the tape length is 90 mm, and the hub diameter is 22 mm, k is equal to 757.7. Further, in the case of C-60 of a metal tape, since the tape thickness is 16 .mu.m, k is equal to 700.4.
From the equations (1), (2) and (3), the following relationship is provided: EQU (L/.theta..sub.L).sup.2 +(L/.theta..sub.R).sup.2 =k
From this equation, L is determined as follows: ##EQU1##
Accordingly, if rotational angles of the supply and take-up reels 11 and 12 within a certain time are measured, it is possible to determine the length L of the tape which has been moved within that time from these rotational angles. Further, if L is divided by the tape running speed at a constant speed, the running amount can be converted to time. It is to be noted that rotational angles .theta..sub.L and .theta..sub.R of the reels can be determined by the reel rotation pulse used in the auto stop.
The approximation means is disclosed in the Japanese Patent Publication No. 13994/83, and this approximation means will now be described.
FIG. 2 is a diagram showing the relationship between a tape running amount and reel rotation number. This figure indicates that according as a tape running amount increases, the rotation number N.sub.R of the take-up reel 12 decreases, and the rotation number N.sub.L of the supply reel 11 increases.
If the reel rotation number per a fixed tape running amount is fixed at any position of the tape, it is possible to determine with ease a tape running amount from the rotation number of the reel. In accordance with the graphical representation at that time, a straight line in parallel to the horizontal axis is provided. In view of this, the approximation means serves to process the graph of FIG. 2 so that it is in correspondence with a straight line in parallel to the horizontal axis, thus to determine a tape running amount.
FIG. 3 is an explanatory view of the approximation means wherein the sum (N.sub.L +N.sub.R) of N.sub.L and N.sub.R and the difference .vertline.N.sub.L -N.sub.R .vertline. therebetween are represented by curves, respectively. In accordance with this figure, it is seen that both the sum of N.sub.L and N.sub.R and the difference therebetween are represented by the curves the left and right halves of which are symmetrical to each other and in which the middle portions are lowered. When the difference is subtracted from the sum, the curve approximate to the straight line of the rotation number M shown in this figure is provided. Namely, the rotation number M is expressed as follows: EQU M.perspectiveto.N.sub.L +N.sub.R -K.vertline.N.sub.L -N.sub.R .vertline.(5)
Namely, the value Obtained by subtracting the difference from the sum of the rotation numbers of the reel can be considered to be approximate to the straight line M. In the above equation, K indicates a ratio between ((N.sub.L +N.sub.R)-M) and (.vertline.N.sub.L -N.sub.R.vertline.). In order to allow the accumulated error over the entire tape length to be small, the area ratio between S1 and S2 of FIG. 3 is used as the value of K.
Namely, since the rotation number M is the sum of the rotation number of the supply reel 11 and that of the take-up reel 12 with respect to a fixed tape running amount at the central portion (at which the rotation number on the supply reel 11 and that on the take-up reel 12 become the same) of the length of the tape, the rotation number of the supply reel 11 and that of the take-up reel 12 can be replaced by the rotation number at the central portion of the tape from the above-mentioned equation (5).
Accordingly, when it is assumed that a fixed tape running amount initially set is 47.6 mm/sec, and the rotation number of the supply reel 11 and that of the take-up reel 12 within a fixed time are represented by N.sub.L1 and N.sub.R1, respectively, the tape running amount L1 is expressed as follows: EQU L1=47.6.times.(N.sub.L1 +N.sub.R1 -K.vertline.N.sub.L1 -N.sub.R1 .vertline.)/M
This tape running amount L1 in terms of the running time t at the time of a constant speed (47.6 mm/sec) is rewritten as follows: EQU t=L1/47.6=(N.sub.L1 +N.sub.R1 -K.vertline.N.sub.L1 -N.sub.R1 .vertline.)/M (6)
Attention is first drawn to the processing by the mathematical means. Since only .sqroot.k can be dealt as a constant as indicated by the above-mentioned equation (4), the remaining parts must be determined by calculation. However, that calculation is a complicated calculation including multiplication, second power and root. 4 bit microcomputers frequently used in cassette decks, etc. at present have no multiplicative instruction, and other 4 bit microcomputers hardly have such an instruction. In addition, instructions for second power, root and division are required. Further, when attention is drawn to the tape running amount at the time of fast forwarding and rewinding, the calculation therefor must be conducted in 5 msec. Such 4 bit microcomputers are hardly able to carry out this calculation while conducting other processing.
On the other hand, in the case of the approximation means, as indicated by the equation (6), the equation to be dealt is more simple than the equation (4) to be dealt by the mathematical means. However, generally at present, detection of the rotation of the reel is carried out by the combination of an eight-pole magnet and a Hall IC. To determine the rotation number, a procedure must be taken to count a time required for one revolution (actually, time required for 1/8 rotation.times.8) to take an inverse number thereof. In the case where such a procedure is taken, the above-mentioned equation (6) is rewritten as follows: EQU t=(1/t.sub.L +1/t.sub.R -K.vertline.1/t.sub.L -1/t.sub.R .vertline.)/M (7)
Also in the case of the approximation means, complicated calculation is required. In the above equation (7), t.sub.L is a time required for one rotation of the supply reel 11, t.sub.R is a time required for one rotation of the take-up reel 12, and K is the above-mentioned constant.
In addition, in order to calculate the accumulated value of the running times, these times t must be repeatedly calculated many times. As a result, the processing increasingly becomes complicated.
As stated above, in both the cases of the above-mentioned mathematical means and approximation means, complicated calculation is required. Thus, the burden on the 4 bit microcomputer would be large.